Final answer:
Using Wien's displacement law, the frequency corresponding to the maximum energy density for a black body at 1000 K is calculated to be approximately 1.035 x 10^14 Hz.
Step-by-step explanation:
To deduce the frequency corresponding to the maximum energy density in the radiation emitted from a black body at a temperature of 1000 K, we can use Wien's displacement law. This law states that the wavelength (λ_max) at which the emission of a blackbody radiation peaks is inversely proportional to the temperature (T) of the blackbody, which can be expressed as λ_max * T = b, where b is Wien's displacement constant (2.8977 x 10-3 m*K).
The frequency (f) can be found by converting the peak wavelength to frequency using the relationship c = λf, where c is the speed of light in a vacuum (approximately 3 x 108 m/s).
Let's calculate the peak wavelength first:
λ_max = b / T
λ_max = (2.8977 x 10-3 m*K) / 1000 K
λ_max = 2.8977 x 10-6 m
Now, convert this to frequency:
f = c / λ_max
f = (3 x 108 m/s) / (2.8977 x 10-6 m)
f = 1.035 x 1014 Hz.
The frequency corresponding to the maximum energy density in the radiation emitted from a black body at 1000 K is approximately 1.035 x 1014 Hz.